Exponential waiting time for filling a large interval in the symmetric simple exclusion process

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1. D.J. Aldous, Markov chains with almost exponential hitting times. Stochastic Process. Appl., Vol. 13, 1982, pp. 305-310. Zbl0491.60077MR671039
2. D.J. Aldous, Probability Approximations via the Poisson Clumping Heuristics. Springer Verlag, 1989. Zbl0679.60013MR969362
3. D.J. Aldous and M. Brown, Inequalities for rare events in time-reversible Markov chains I in M. Shaked and Y. L. Tong, Stochastic InequalitiesIMS Lecture Notes, Vol. 22, 1992, pp. 1-16. MR1228050
4. D.J. Aldous and M. Brown, Inequalities for rare events in time-reversible Markov chains II. Stochastic Processes Appl., Vol. 44, 1993, pp. 15-25. Zbl0812.60054MR1198660
5. R. Arratia and S. Tavare, Review of Probability Approximations via the Poisson Clumping Heuristic by D. Aldous and Poisson Approximations by A. D. Barbour, L. Holst and S. Janson, Ann. Probab., Vol. 21, 1993, pp. 2269-2279. 
6. V. Belitsky, An upper bound of density for two-particle annihilating exclusion. J. Stat. Phys., Vol. 73, No.3/4, 1993, pp. 671-694. Zbl1102.60322MR1251659
7. V. Belitsky, Asymptotic behavior of density for two-particle annihilating exclusion. Preprint, 1994. Zbl1080.60513MR1315236
8. R. Bellman and T.E. Harris, Recurrence times for the Ehrenfest model. Pacific J. Math., Vol. 1, 1951, p. 179. Zbl0045.07802MR45323
9. M. Cassandro, A. Galves, E. Olivieri and M.E. Vares, Metastable behavior of stochastic dynamics: a pathwise approachJ. Stat. Phys., Vol. 35, 1984, pp. 603-633. Zbl0591.60080MR749840
10. R. Cogburn, On the distribution of first passage and return times for small sets. Ann. Probab., Vol. 13, 1985, pp. 1219-1223. Zbl0591.60063MR806219
11. P. Collet, A. Galves and B. Schmitt, Unpredictability of the occurrence time of a long laminar period in a model of temporal intermittency. Ann. Inst. H. Poincaré, Section A, Vol. 57, 3, 1992, pp. 319-331. Zbl0756.60022MR1185337
12. P.A. Ferrari, A. Galves and C. Landim, Exponential waiting time for a big gap in a one dimensional zero range process. Ann. Probab., Vol. 22, 1, 1994, pp. 284-288. Zbl0793.60108MR1258878
13. A. Galves, F. Martinelli and E. Olivieri, Large-density fluctuations for the one-dimensional supercritical contact processJ. Stat. Phys., Vol. 55, 1989, pp. 639-648. Zbl0713.60109MR1003532
14. T.E. Harris, First passage and recurrence distributions. Trans. Amer. Math. Soc., Vol. 73, 1953, pp. 471-486. Zbl0048.36301MR52057
15. T.E. Harris, Additive set valued Markov processes and graphical methods. Ann. Probab., Vol. 6, 1978, pp. 355-378. Zbl0378.60106MR488377
16. C. Kipnis and C. Newman, The metastable behavior of infrequently observed, weakly random, one-dimensional diffusion processes. SIAM J. Appl. Math., Vol. 45, 1985, p. 972. Zbl0592.60063MR813459
17. D.V. Korolyuk and D. S. SIL'VESTROV, Entry times into asymptotically receding domains for ergodic Markov chains. Theory Prob. Appl., Vol. 19, 1984, pp. 432-442. Zbl0533.60079
18. J.L. Lebowitz, R.H. Schonmann, On the asymptotics of occurrence times of rare events for stochastic spin systems. J. Stat. Phys., Vol. 48, 1987, pp. 727-751. Zbl1084.82521MR914904
19. T.M. Liggett, Interacting Particle Systems. Springer, Berlin, 1985. Zbl0559.60078MR776231
20. S.L. Lu and H-T. Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics. Commun. Math. Phys., Vol. 156, 1993, pp. 399-433. Zbl0779.60078MR1233852
21. R. Schonmann, An approach to characterize metastability and critical droplets in stochastic Ising models. Ann. Inst. H. Poincaré, Section A, Vol. 55, 1991, pp. 591-600. Zbl0741.60103MR1139535
22. F. Spitzer, Interaction of Markov processes. Adv. Math., Vol. 5, 1970, pp. 246-290. Zbl0312.60060MR268959

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